1. How to explore a system? Photons Electrons Atoms Electrons Photons Atoms

2. How to explore a system? Photons Electrons With different kinetic energies

3. Detect the charged particles for a given energy range with good energy (and space) resolution Electron Energy Analyzers Retarding Field Analyzer (RFA) Cylindrical Mirror Analyzer (CMA) Hemispherical Analyzer (HA)

4. Separate the electrons with a defined energy band Electron Energy Analyzers Electron Energy (eV) N(E) E0E0 E 0 + ΔE Energy distribution curve: response of the system

5. Retarding Field Analyzer (RFA) V0V0

6. N(E) V 0 = Retarding potential E 0 = eV 0 = Pass energy Current to screen To obtain N(E) one has to differentiate V0V0 Electron Energy (eV) N(E) E0E0 E 0 + ΔE

7. Retarding Field Analyzer (RFA) Modulation

8. First harmonic Second harmonic N(E) dN(E)/dE RFA: poor sensitivity and energy resolution No angular resolution

9. Electrostatic deflection analyzers Energy band pass Cylindrical Mirror Analyzer (CMA) Hemispherical Analyzer (HA) Dispersing field Deflection is function of electron energy v1v1 v1v1 v2v2 - + Electrons have angular spread around the entrance direction Electrons with same v will be deflected by different amounts Degradation of energy resolution Concept

10. Cylindrical Mirror Analyzer (CMA) V=deflecting voltage between cylinders e - energy consider an e- arriving at an angle  0 with e - energy inside cylinder work of the e.m. field on e - e - cross the inner cylinder through a slit experience the field –V of the outer cylinder go to second slit and and arrive in F

11. Cylindrical Mirror Analyzer (CMA) Electrons with same E will be deflected by different amounts depending on the entrance angle The trajectory for which the e- is focussed is a solution of the equation of motion (cyl. coord.) The maximum deflection depends on the entrance angle, and shows that K 0 depends also on  focussing condition

12. A single focussing length L correspond to different acceptance angles (see curve (c)) High sensitivity with one pass energy The numerical solution shows that for a single K 0 there are two values of entrance angle This means that in general there are two focussing distances For K 0 = 1.31 the two focal distances merge into one Cylindrical Mirror Analyzer (CMA) L = 6.130 r 1

13. Cylindrical Mirror Analyzer (CMA) The emission angle determines three main factors (a) source-image distance on the common cylinders axis (L) (b) the deflecting voltage for particles with energy E (c) the required ratio between the cylinders radii For  0 = 42°18.5' the first spherical aberration term = 0 L

14. For small  and small  E, the shift in the axis crossing point is (Taylor series) One looks for  L  0 Base resolution Cylindrical Mirror Analyzer (CMA) r 1 = inner cylinder Neglecting the product

15. Transmission = fraction of space in front of the sample intercepted by the analyser analyser transmission Cylindrical Mirror Analyzer (CMA) For a fixed slit, T does not depend on energy

16. For a given slit, T does not depend on energy while  E B  E peak area  (T x  E B ) Electron Energy (eV) N(E) E0E0 E 0 + ΔE B Peak area  N(E)xE Cylindrical Mirror Analyzer (CMA) So the energy resolution is not constant with E The spectrum contains the intensity-energy response function of the analyser but (T x  E B )  E The image of the source can be reduced by inserting a slit before the focus that reduces the coefficients of  3 by a factor of 4 Finite source + ring slit of width W and radius r 1

17. Two spherical electrodes Concentric Hemispherical Analyzer (CHA) 1/r electrostatic potential Electrons are injected with energy eV 0 at slit S in the point corresponding to radius R 0 The condition to allow e - to describe the central orbit is (point source) Focussing condition in F For R 1 =115 R 2 =185 mm K = 1.013

18. e- forming angle  with tangential direction Concentric Hemispherical Analyzer (CHA) The resolution is mainly determined by the central hemispherical radius R 0 =150 mm W 1 = W 2 = 3 mm e- with energy  E with respect to E 0 Considering two slits of width W 1 and W 2 Base resolution Shift in the radial position R 0 =150 mm W 1 = W 2 = 1 mm

19. Worse than CMA (lower transmission and resolution)??? Transmission of the analyser Concentric Hemispherical Analyzer (CHA) If the sample is at the position of the slit W 1, we assume W 1 = 0 and neglect  so the angular acceptance in the plane depends on the slit W 2 We also have to consider the angular acceptance in the plane perpendicular to the screen (  ) Transmission In analogy to the CMA

20. Concentric Hemispherical Analyzer (CHA) Problem: sample cannot be at position of slit 1 solutions Reduce the analyzer angle to 150° Use lenses to focus beam at slit 1 r = source radius  = cone semiangle of source E = e - energy at the source r p = source image at entrance slit W 1  = cone seminagle of image E p = e - energy at the image Helmoltz-Lagrange equation Lens magnification Retarding ratio  = cone semiangle of source defined by the lens

21. Concentric Hemispherical Analyzer (CHA) What is defining the transmission of the analyser? Consider the cone with semiangle  1.The lens defines the transmission 2.The lens defines the transmission in  and the spectrometer in  3.The spectrometer defines the transmission The CHA is designed to accept  of about 4-5° (similar to  = 5)

22. Electrostatic lenses Optical ray refractionElectron refraction e speed Refraction index electrostatic potential The potential changes abruptly at the interface: only the perpendicular component of the momentum changes Snell’s law: n 1 sin  1 = n 2 sin  2

23. Electrostatic lenses For real lenses there are no abrupt changes in the potential, as shown in the figure But one can assume the asymptotic behavior of the electron trajectories to make use of the lens equations Equipotential lines e path Transverse magnification Angular magnification Helmoltz-Lagrange equation Conservation of brightness

24. Electron lenses formed using metallic apertures. Electrostatic lenses Lenses has the effect to change the kinetic energy of the beam Focussing DefocussingFocussing

25. Electrostatic deflection analyzers CHA Energy resolution E 0 = pass energy ΔE B = Emin-Emax transmitted s = slit width ,  angular apertures ABCn Cylindrical mirror2.2/l5.5503 Cylindrical deflector 127°2/r4/312 Spherical deflector 180°1/r102 CMA

26. Electrostatic deflection analyzers Geometry of the acceptance slit is very different CHA CMA 5°  6° 42.3° Small signal Compatible with simple electrostatic aperture and tube lenses Long focal distance Radius 100 - 150 mm Res. Power about 1000-5000 Working distance about 25-50 mm Large signal Non compatible with simple electrostatic aperture and tube lenses Short focal distance Cyl diam 100 - 150 mm Res. Power about 200 Working distance about 5 mm

27. Electrostatic deflection analyzers Detection mode Single Scan over voltages acquiring counts at each energy Scan over voltages acquiring the position and therefore the energy of the electrons with different trajectories Multi E1E1 E2E2 E3E3 E(V)

28. Electrostatic deflection analyzers Detection mode Scan over voltages acquiring the position and therefore the energy of the e - with different trajectories Multi Channeltron Channelplates + ccd camera

29. Electrostatic deflection analyzers Mode of operation No pre-retarding potential Vary E 0 with Vscan  E B is increasing with energy Pre-retarding potential Vary the pre-retarding potential and not E 0  E B is constant

30. Hemispherical Analyzer of Electron Kinetic Energy

31. Lay-out of an Electron Spectroscopy Experiment Based onto a Double-Pass Cylindrical Mirror Analyzer

32. Hemispherical Analyzer of Electron Kinetic Energy with Entrance Optics Designed for Lateral Resolution

33. Electron Source and Energy Monochromator and Electron Kinetic Energy Analyzer HREELS Apparatus

34. Electron Multiplier Detection efficiency 80 % Gain 10 8

35. Microchannel plates Thin Si-Pb oxide glass wafers Channel walls act as electron multipliers Channel density  10 5 cm -1 Detection efficiency 80 % Gain 10 5 - 10 8